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<p>下面给出在不同数据范围下，代码的时间复杂度和算法该如何选择：</p>
<ul>
<li>n≤30, 指数级别, dfs+剪枝，状态压缩dp</li>
<li>n≤ 100 =&gt; O($n^3$)，floyd，dp，高斯消元</li>
<li>n≤ 1000 =&gt; O($n^2$)，O($n^2log_n$)，dp，二分，朴素版 ijkstra、朴素版Prim、Bellman-Ford</li>
<li>n≤ 10000 =&gt; O(n∗$\sqrt{n}$ )，块状链表、分块、莫队</li>
<li>n≤ 100000 =&gt; O(n$log_n$) =&gt; 各种sort，线段树、树状数组、set/map、heap、拓扑排序、dijkstra+heap、prim  +heap、Kruskal、spfa、求凸包、求半平面交、二分、CDQ分治、整体二分、后缀数组、树链剖分、动态树</li>
<li>n≤ 1000000 =&gt; O(n), 以及常数较小的 O(n$log_n$)O(n$log_n$) 算法 =&gt; 单调队列、 hash、双指针扫描、并查集，kmp、AC自动机，常数比较小的 O(n$log_n$)O(n$log_n$) 的做法：sort、树状数组、heap、dijkstra、spfa</li>
<li>n≤ 10000000 =&gt; O(n)，双指针扫描、kmp、AC自动机、线性筛素数</li>
<li>n≤ $10^9$=&gt; O($\sqrt{n}$)，判断质数</li>
<li>n≤ $10^{18}$ =&gt; O($log_n$)，最大公约数，快速幂，数位DP</li>
<li>n≤$10^{1000}$ =&gt; O($(log_n)^2$)，高精度加减乘除</li>
<li>$n≤10^{100000}$=&gt; $O(log_k×loglog_k)$，k表示位数O($logk×loglog_k$)，k表示位数，高精度加减、FFT/NT</li>
</ul>
<p>作者：yxc<br>链接：<a target="_blank" rel="noopener" href="https://www.acwing.com/blog/content/32/">https://www.acwing.com/blog/content/32/</a><br>来源：AcWing<br>著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。</p>
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